The basic income would replace virtually all current state benefits. This would already be sufficient to pay for approximately one third of the basic income. In addition to this there would be a dramatic decrease in the cost of bureaucracy and in administration as everybody would receive the basic income. There would be no need to employ the people who currently check whether those who claim unemployment benefit are really unemployed. This money would also be transferred to the basic income.
Secondly there would be a restructuring of the tax system. VAT would replace all existing taxes and would be increased to around 50%. Income tax is incredibly difficult and inefficient as it is so easy to avoid. The state wastes millions in tax evasion and in trying to crack down on fraud. But VAT is unavoidable. Consequently the state would receive more and would pay less for the administration. This increase in revenue would also contribute towards the basic income.
Finally it is reasonable to expect an increase in productivity. The basic income would lead to a transfer of power from employer to employee, as people would no longer be dependent on work for pay. As a result people would be able to chose jobs which they enjoy and in which they are more motivated, and this would lead to an increase in productivity. With the cost of labour increasing, the incentive to invest in new technologies would increase and once again this would contribute to more productive businesses.